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XAT 2022 — QA & DI Question 6

Number TheoryEasy

The sum of the cubes of two numbers is 128, while the sum of the reciprocals oftheir cubes is 2. What is the product of the squares of the numbers?

Answer & solution

Correct answer: 16

  • A

    64

  • B

    256

  • 16

  • D

    48

  • E

    32

Solution

Considering the two numbers to a, b :
We were given that:

a3 + b3 = 128

1a3 + 1b3 = 2

(a3+b3a3.b3) = 2 = 128k

k = 64.

Hence a3 . b3 = 64

a*b = 4 and a2 .b2 = 16

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XAT 2022 QA & DI Q6: The sum of the cubes of two numbers is 128, while the sum of the reciprocals oftheir cubes is 2. What is the p — Solution | TheCATExam